Two-phase fluid flow in a porous tube: a model for blood flow in capillaries

A theoretical study of blood flow, under the influence of a body force, in a capillary is presented. Blood is modeled as a two-phase fluid consisting of a core region of suspension of all erythrocytes, represented by a micropolar fluid and a plasma layer free from cells modeled as a Newtonian fluid. The capillary is modeled as a porous tube consisting of a thin transition Brinkman layer overlying a porous Darcy region. Analytical expressions for the pressure, microrotation, and velocities for the different regions are given. Plots of pressure, microrotation, and velocities for varying micropolar parameters, hydraulic resistivity, and Newtonian fluid layer thickness are presented. The overall system was found to be sensitive to variations in micropolar coupling number. It was also discovered that high values of hydraulic resistivity result in an overall slower velocity of the micropolar and Newtonian fluid.     

Time periodic electroosmotic flow of micropolar fluids through microparallel channel

The time periodic electroosmotic flow of an incompressible micropolar fluid between two infinitely extended microparallel plates is studied.The analytical solutions of the velocity and microrotation are derived under the Debye-H(u|¨)ckel approximation.The effects of the related dimensionless parameters,e.g.,the micropolar parameter,the frequency,the electrokinetic width,and the wall zeta potential ratio of the upper plate to the lower plate,on the electroosmotic velocity and microrotation are investigated.The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1.The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid.However,the dependence of the microrotation on the related parameters mentioned above is complex.In order to describe these effects clearly,the dimensionless microrotation strength and the penetration depth of the microrotation are defined,which are used to explain the variation of the microrotation.In addition,the effects of various parameters on the dimensionless stress tensor at the walls are studied.     

Lubrication theory for micropolar fluids and its application to a journal bearing with finite length

In this paper, the field equation of micropolar fluid with general lubrication theory assumptions is simplified into two systems of coupled ordinary differential equation. The analytical solutions of velocity and microrotation velocity are obtained. Micropolar fluid lubrication Reynolds equation is deduced. By means of numerical method, the characteristics of a finitely long journal bearing under various dynamic parameters, geometrical parameters and micropolar parameters are shown in curve form. These characteristics are pressure distribution, load capacity, coefficient of flow flux and coefficient of friction. Practical value of micropolar effects is shown, so micropolar fluid theory further closes to engineering application.     

Electroosmotic oscillatory flow of micropolar fluid in microchannels: application to dynamics of blood flow in microfluidic devices

The electroosmotic flow of a micropolar fluid in a microchannel bounded by two parallel porous plates undergoing periodic vibration is studied. The equations for conservation of linear and angular momentums and Gauss' s law of charge distribution are solved within the framework of the Debye-H¨uckel approximation. The fluid velocity and microrotation are assumed to depend linearly on the Reynolds number. The study shows that the amplitude of microrotation is highly sensitive to the changes in the magnitude of the suction velocity and the width of the microchannel. An increase in the micropolar parameter gives rise to a decrease in the amplitude of microrotation. Numerical estimates reveal that the microrotation of the suspended microelements in blood also plays an important role in controlling the electro-osmotically actuated flow dynamics in microbio-fluidic devices.     

NonLinearly Elastic Membrane Model For Heterogeneous Shells by Using a New Double Scale Variational Formulation: A Formal Asymptotic Approach

This paper is concerned with the asymptotic analysis of shells with periodically rapidly varying heterogeneities. The asymptotic analysis is performed when both the periods of changes of the material properties and the thickness of the shell are of the same orders of magnitude. We consider a shell made of Saint Venant–Kirchhoff type materials for which we justify a new two-scale variational formulation. We assume that both the data and the displacement field admit a formal asymptotic expansion with a negative order of the leading term. We prove that the lowest order term of the displacement field must be of order zero. When the space of nonlinear inextensional displacement is reduced to , this displacement field is a solution of a two-dimensional membrane model which is obtained by solving two coupled problems. The first, posed on the middle surface of the shell is two-dimensional and global and the second, posed on the periodicity cell, is three-dimensional and local.     

A transient natural convection of micropolar fluids over a vertical cylinder

A transient free convective boundary layer flow of micropolar fluids past a semi-infinite cylinder is analysed in the present study. The transformed dimensionless governing equations for the flow, microrotation and heat transfer are solved by using the implicit scheme. For the validation of the current numerical method heat transfer results for a Newtonian fluid case where the vortex viscosity is zero are compared with those available in the existing literature, and an excellent agreement is obtained. The obtained results concerning velocity, microrotation and temperature across the boundary layer are illustrated graphically for different values of various parameters and the dependence of the flow and temperature fields on these parameters is discussed. An increase in the vortex viscosity tends to increase the magnitude of microrotation and thus decreases the peak velocity of fluid flow. An increase in the vortex viscosity in micropolar fluids is shown to decrease the heat transfer rate.     

Convective stability analysis of a micropolar fluid layer by variational method

This paper studies Rayleigh-Bénard convection of micropolar fluid layer heated from below with realistic boundary conditions. A specific approach for stability analysis of a convective problem based on variational principle is applied to characterize the Rayleigh number for quite general nature of bounding surfaces. The analysis consists of replacing the set of field equations by a variational principle and the expressions for Rayleigh number are then obtained by using trial function satisfying the essential boundary conditions. Further, the values of the Rayleigh number for particular cases of large and small values of the microrotation coefficient have been obtained. The effects of wave number and micropolar parameter on the Rayleigh numbers for onset of stationary instability for each possible combination of the bounding surfaces are discussed and illustrated graphically. The present analysis establishes that the nature of bounding surfaces combination and microrotation have significant effect on the onset of convection.     

Boundary-layer flow of a micropolar fluid due to a stretching wall

Summary  A Theoretical analysis is carried out to study the boundary-layer flow over a continuously moving surface through an otherwise quiescent micropolar fluid. The transformed boundary-layer equations are solved numerically for a power-law surface velocity using the Keller-box method. The effects of the micropolar K and exponent m parameters on the velocity and microrotation field as well as on the skin-friction group are discussed in a detailed manner. It is shown that there is a near-similarity solution of this problem. The accuracy of the present solution is also discussed. Accepted for publication 1 April 1996     

Free convection from a truncated cone subject to constant wall heat flux in a micropolar fluid

The paper studies the problem of free convection about a vertical frustum of a cone in a micropolar fluid. It is assumed that the flow is laminar, steady and the wall is subjected to a constant heat flux and the angle of the frustum of the cone is large enough so that the transverse curvature effects are negligible. Under these assumptions, the governing boundary layer equations subject to appropriate boundary conditions are transformed into a set of equations of parabolic type, that are solved using the local non-similarity method. The space of parameters contains the Prandtl number Pr, the micropolar parameter Δ and the microrotation parameter n. Numerical solutions are obtained by varying Pr from 6.7 to 100, Δ from 0 (Newtonian fluid) to 2 and considering two values of n with physical significance (0 and 0.5). Flow and heat transfer characteristics are determined and are shown in graphs. The results are discussed and compared at some extent with those reported by the present author in a previous study (Postelnicu in Int. J. Eng. Sci. 44:672–682, 2006) on the isothermal case.     

Integral equation methods in plane asymmetric elasticity

The boundary integral equation method is used to solve the interior and exterior Dirichlet, Neumann and mixed problems of plane micropolar elasticity. In the exterior case, a specific far-field pattern for the displacements and microrotation is introduced without which the classical scheme fails to work. Finally, we discuss the direct method and establish a connection with results obtained previously.     

Axisymmetric free vibrations of infinite thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Axisymmetric free vibrations of infinite micropolar thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Unsteady Couette flow of a micropolar fluid with slip

The unsteady Couette flow of an isothermal incompressible micropolar fluid between two infinite parallel plates is investigated. The motion of the fluid is produced by a time-dependent impulsive motion of the lower plate while the upper plate is set at rest. A linear slip, of Basset type, boundary condition on both plates is used. Two particular cases are discussed; in the first case we have assumed that the plate moves with constant speed and in the second case we have supposed that the plate oscillates tangentially. The solution of the problem is obtained in the Laplace transform domain. The inversion of the Laplace transform is carried out numerically using a numerical method based on Fourier series expansion. Numerical results are represented graphically for the velocity, microrotation, and volume flux for various values of the time, slip and micropolar parameters.     

Secondary flow induced by the rotation of two concentric spheres about their common diameter in micropolar fluids

Summary In this paper, we have studied the secondary flow induced in a micropolar fluid by the rotation of two concentric spheres about a fixed diameter. The secondary flow exhibits behaviour commonly observed in visco-elastic fluids. In particular we have obtained the expressions for microrotation vector. Numerical results have been obtained for a number of values of relative rotations of the two spheres for a chosen set of values of fluid parameters. The results are presented graphically and compared with the previous investigations.     

Moving load response in micropolar thermoelastic medium without energy dissipation possessing cubic symmetry

The steady state response of a micropolar thermoelastic medium without energy dissipation possessing cubic symmetry due to a moving load has been studied. Fourier transform has been employed and the transform has been inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution have been compared for micropolar cubic crystal and micropolar isotropic solid. The numerical results are illustrated graphically for a particular material. Some special cases have also been deduced.     

Time harmonic sources at micropolar thermoelastic medium possessing cubic symmetry with one relaxation time

The response of a micropolar thermoelastic medium possessing cubic symmetry with one relaxation time due to time harmonic sources has been investigated. Fourier transform has been employed and the transform has been inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution have been compared for micropolar cubic crystal and isotropic micropolar solid. The numerical results are illustrated graphically for a particular material. Some special cases have also been deduced.     

Deformation due to time harmonic sources in micropolar thermoelastic medium possessing cubic symmetry with two relaxation times

The response of a micropolar thermoelastic medium possessing cubic symmetry with two relaxation times due to time harmonic sources is investigated. Fourier transform is employed and the transform is inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution are compared for micropolar cubic crystal and micropolar isotropic solid. The numerical results are illustrated graphically for a particular material. Some special cases are also deduced.     

Mixed convection flow of a micropolar fluid over a stretching sheet

The mixed convective flow of a steady, incompressible micropolar fluid over a stretching sheet has been studied. This situation may arise in polymer technology involving the stretching of plastics sheets. The resulting system of non-linear ordinary coupled differential equations has been solved by the finite element method, using the variational Ritz model. Numerical results obtained for velocity, microrotation and temperature distributions are shown graphically. It was found that an increase in the micropolar parameter leads to a faster rate of cooling of the sheet. Also the velocity increases with an increase in micropolar effects. Microrotation effects are much smaller for the no-spin boundary condition as compared to the other boundary condition which assumes that the gyration vector is identical to the angular velocity of the fluid. Received on 9 February 1998     

On hydrodynamic boundary conditions for microstructural fluids

Various types of boundary conditions used when investigating microrotation are analysed. A boundary condition for studying microstructural fluid flows, which depends on experimental parameters, is suggested. To illustrate the result, expressions are derived for the velocity and microrotation of a micropolar fluid between two coaxial cylinders with a constant relative speed of rotation.     

RESTUDY OF COUPLED FIELD THEORIES FOR MICROPOLAR CONTINUA (Ⅰ)──MICROPOLAR THERMOELASTICITY

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